Todd Akin and his wife Lulli talk with reporters at the Missouri State Fair last week. Photograph: Orlin Wagner/AP

The Republican congressman at the centre of a row over remarks he made about rape has once again insisted that he will not quit the Missouri Senate race and described the pressure on him to quit as "an overreaction".

Todd Akin said he would be ignoring a state election deadline this evening that would have provided an opportunity to exit easily.

He is under huge pressure from the Republican leadership to stand down from the closely fought Missouri race. His decision to press on will be viewed with dismay by senior members of the party.

Speaking live on the Mike Huckabee radio show on Tuesday, he said that he was receiving a large amount of support from small, grassroots supporters, including donations, and this helped counter-balance withdrawal of support from Republican leaders. "I just misspoke one word in one sentence on one day," Akin said.

An unusual coalition of senior and grassroots Republicans has been making a concerted effort to get him to quit.

Tea Party groups, some of which helped Akin secure victory in the primary last week, urged him to go. There were similar calls Monday by presidential challenger Mitt Romney and his running mate Paul Ryan, congressional leaders and conservative talk show hosts.

Under state election law, Akin would face no financial penalties if he pulls out by 6pm ET on Tuesday, and the party would be free to pick an alternative. If he goes beyond that time, the next date for withdrawal would be 25 September, but that would require a court order to allow him leave the race.

Leaving it until September could also mean he would face significant financial penalties, such as reimbursing the cost of reprinting ballot papers or other election material.

But the Republicans' difficulties on abortion are unlikely to go away even if Akin does quit. On Tuesday, as the leadership turned up the heat on Akin, the party approved language in its platform calling for a constitutional amendment banning abortion with no explicit exemptions in cases of rape and incest.

Meanwhile, another Republican congressman, Steve King of Iowa, inflamed the row, defending Akin and suggesting that he'd never heard of a woman getting pregnant from statutory rape or incest.

Talking Points Memo on Monday reported that King told Iowa radio station KMEG-TV reported him saying: "Well I just haven't heard of that being a circumstance that's been brought to me in any personal way and I'd be open to discussion about that subject matter."

The Missouri seat held by Democrat Claire McCaskill is regarded by Republicans as the top target in the campaign to take control of the Senate. McCaskill, who has used the row to portray Akin as an extremist, is urging him to stay in the race.

The Republican Senate campaign committee and conservative Super Pacs have withdrawn about $10m in financial support for Akin. The last remaining hope for Akin is to attract donations from individual donors.

If Akin quits, he could be replaced either by Jim Brunner, a businessman who came second in the primary with 30% – 6% behind Akin – or Sarah Steelman, a former state treasurer, who took 29%. Brunner has already been sounding out party members about replacing Akin.

Public Policy Polling, in a survey conducted on Monday night, showed the row has not had any significant impact on voting intentions yet. Akin is leading McCaskill 44% to 43%, almost unchanged from May when he was ahead 45% to 44%.

It may be that the poll was conducted too soon to fully register any unease with Akin.

As well as possible repercussions for the Senate race, Democrats also see Akin as useful in highlighting differences between the Obama-Biden ticket and the Romney-Ryan ticket on abortion.

In the light of the row, there will be pressure to change the draft to include exceptions for rape and incest.